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#!/usr/bin/env python
import openturns as ot
import openturns.testing as ott
ot.TESTPREAMBLE()
# We create a numerical math function
dim = 2
# event
f = ot.SymbolicFunction(["x0", "x1"], ["5.0-x1-0.5*(x0-0.1)^2"])
dist = ot.Normal(dim)
X = ot.RandomVector(dist)
Y = ot.CompositeRandomVector(f, X)
event = ot.ThresholdEvent(Y, ot.Less(), 0.0)
# solver
solver = ot.Cobyla()
solver.setMaximumCallsNumber(1000)
solver.setMaximumAbsoluteError(1.0e-10)
solver.setMaximumRelativeError(1.0e-10)
solver.setMaximumResidualError(1.0e-10)
solver.setMaximumConstraintError(1.0e-10)
# algorithm
start_pt = [0.0] * dim
algo = ot.MultiFORM(solver, event, start_pt)
algo.setMaximumDesignPointsNumber(4)
algo.run()
result = algo.getResult()
print("result=", result)
pf_multi = result.getEventProbability()
ott.assert_almost_equal(pf_multi, 0.00281872, 1e-4, 1e-4)
print("event probability=%.6f" % pf_multi)
n_design_pts = len(result.getFORMResultCollection())
print("n design points:", n_design_pts)
assert n_design_pts == 2, "should get 2 design points"
for form_result in result.getFORMResultCollection():
print("-" * 50)
print(
"generalized reliability indexes=", form_result.getGeneralisedReliabilityIndex()
)
print("pf=", form_result.getEventProbability())
print("standard space design points=", form_result.getStandardSpaceDesignPoint())
print("physical space design points=", form_result.getPhysicalSpaceDesignPoint())
print(
"is standard point origin in failure space? %s"
% (form_result.getIsStandardPointOriginInFailureSpace() and "true" or "false")
)
print("importance factors=", form_result.getImportanceFactors())
print("Hasofer reliability indexes=", form_result.getHasoferReliabilityIndex())
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